Which of the following statements is/are correct about irrational numbers? (A) The sum of two rational numbers is always irrational. (B) is an irrational number. (C) The value of √49 is an irrational number. (D) The value of √5 is an irrational number. Choose the correct answer from the options given below: Option 1: (A),(B) and (C) only Option 2: (A), (B) and (D) only Option 3: (A), (B), (C) and (D) Option 4: (B) and (D) only

Answer: (B) and (D) only. Solution: Rationals are closed under addition, so the sum of two rationals is always rational, making (A) false. √49 = 7, a rational number, so (C) is false. is non-terminating and non-repeating and 5 is not a perfect square, so (B) and (D) are true.

Quantitative Reasoning

Number System

Easy

Which of the following statements is/are correct about irrational numbers?

(A) The sum of two rational numbers is always irrational.

(B) $\pi$ is an irrational number.

(C) The value of $\sqrt{49}$ is an irrational number.

(D) The value of $\sqrt{5}$ is an irrational number.

Choose the correct answer from the options given below:

(A),(B) and (C) only

(A), (B) and (D) only

(A), (B), (C) and (D)

(B) and (D) only

✅ Correct Option: 4

Rationals are closed under addition, so the sum of two rationals is always rational, making (A) false. $\sqrt{49} = 7$ , a rational number, so (C) is false. $\pi$ is non-terminating and non-repeating and 5 is not a perfect square, so (B) and (D) are true.

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The sum of the perfect squares between 120 and 300 is .

2026: 31 May Shift 1

Match the LIST-I with LIST-II

LIST-I (Number)	LIST-II (Unit digit of the number)
A. $4^{425}$	I. 6
B. $4^{1024}$	II. 4
C. $133^{63} \times 4^{49}$	III. 3
D. $3^{81}$	IV. 8

Choose the correct answer from the options given below:

2023: 5 June Shift 2

Simplify : $2 \times [4 - \{2 - (2-3) - (2+3)\} - 1] - 5 \times [-3 - (3-2)]$

2026: 14 May Shift 2

The difference between the two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the reminder is 15. Find the smallest number?

2022: 23 Aug Shift 1

Find the greatest number that will divide 38, 88 and 163 so as to leave the same remainder in each case

2022: 20 Aug Shift 1

Find the value of $\left(\sqrt[3]{\frac{125}{27}} - \sqrt[3]{\frac{512}{729}}\right) \div \sqrt[3]{\frac{64}{5832}}$ is

Solution

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